1. Field of the Invention
The present invention relates to an animation method of deformable objects, in particular, by modeling a deformable object into oriented material points and generalized springs. More particularly, the present invention animates a deformable object by modeling the deformable object into a structure of material points connected with generalized springs, calculating force and torque applied to the material points by the springs and external force, and integrating the force and torque to obtain new positions and postures of the material points.
2. Description of the Related Art
Recently, three dimensional (3 D) animation is being more widely used owing to the performance enhancement and cost reduction of 3 D graphic accelerator cards in use for computers such as a work station and a Personal Computer (PC). As a result, real time calculation of physical simulation, which was impossible in the past owing to long calculation time, is enabled thereby creating a new field of physically based simulation in 3 D animation. In case of 3 D games, there is a trend that such physically based simulation is recently used together with conventional motion capture technique in order to impart smooth animation to the human body of a main character so that the main character interacts realistically and physically with virtual objects. In particular, an animation of deformable objects such as hair or clothes of a game character waving or fluttering in the wind breathes vividness into game contents.
Deformable object animation in contrast with fixed or rigid body animation refers literally to animation of objects which are not fixed in shape. Representative examples of deformable objects may include one dimensional objects such as hair, two dimensional objects such as cloth, clothes and flag, and three dimensional objects such as jelly and tube.
Current deformable object animation widely adopts a mass-spring model. For example, this technique models a deformable object into a group of material points connected by springs, calculates forces applied to the material points via the springs, and integrating the forces to obtain new positions to animate the deformable object. The springs adopted in this technique are positioned in a three dimensional space; nevertheless they perform one dimensional motions.
FIG. 1 schematically illustrates a mass-spring model of the prior art. Referring to FIG. 1, the mass-spring model of the prior art includes basically two material points 101 and 102 and a spring 103 for connecting the material points 101 and 102. The reference numeral 104 in FIG. 4 designates the length L of the spring 103. Expanding or contacting the spring 103 generates a force proportional to the length variation of the spring. When a spring is transformed, a force reacting on the spring is expressed mathematically as equation 1:F=−k*x  Equation 1,wherein k is spring constant, and x is the length variation of the spring.
If the two material points 101 and 102 are connected with the spring, they are applied with equal but opposite forces owing to the law of action-reaction. According to Equation 1, it would be understood that the forces applied to the material points are proportional to the length variation of the spring but not related to the spatial posture of the spring.
Accordingly, when the conventional mass-spring model is utilized to constitute a one dimensional deformable object such as a mobile, the one dimensional deformable object is applied with external force such as gravity to collapse the shape of the one dimensional deformable object, without any force for restoring the original shape of thereof. For example, on the assumption that gravity is applied downward in a one dimensional deformable object such as a mobile, when the uppermost material point of the one dimensional deformable object is fixed, the remaining material points are aligned on a line in the direction of gravity so that the one dimensional deformable object loses its original shape. Forming a two dimensional deformable object such as an uneven cloth via the conventional mass-spring model also does not provide any restoring force to maintain the original uneven shape of the two dimensional deformable object, and thus external force collapses the shape of the two dimensional deformable object. Also, even though a three dimensional deformable object in the shape of a cube is formed based upon the conventional mass-spring model, this deformable object cannot maintain its cubic shape owing to a principle applied thereto that is similar to the above explanation.
Because there are problems in maintaining the original shape of a deformable object, the afore-described conventional deformable object animation using the mass-spring model has a drawback to further have a spring for maintaining the structure of the deformable object in addition to an intuitive structure for expressing the shape of the deformable object. That is, because a spring structure becomes more sophisticated in proportion to the complexity of a deformable object subject to mass-spring modeling, it is difficult for a user to establish the spring structure.
As a previous patent of the conventional deformable object animation, there is disclosed U.S. Pat. No. 6,532,014 (registered on Mar. 11, 2003) entitled “Cloth Animation Modeling.” This previous patent decouples longitudinal nodes from latitudinal nodes and connects splines with springs to calculate forces between the nodes in order to execute cloth modeling. However, this previous patent has limited effects since it restricts the object of animation to cloth among deformable objects.
Another previous patent of the conventional deformable object animation discloses U.S. Pat. No. 5,777,619 (registered on Jul. 7, 1998) entitled “Method for Simulating Hair Using Particle Emissions. ”This previous patent is characterized in that the hair is simulated as a particle system in contemplation that the shape of a hair is similar to the trajectory of a particle emission. Although this previous patent is effective to the hair among deformable objects subject, there is a drawback it is not suitable to simulation of other deformable objects since particles are not connected together.
Also, there is a previous document about the conventional deformable object animation entitled “Large Steps in Cloth Simulation” (Proc. of SIGGRAPH 98, pp 43–54, 1998), proposed by D. Baraff and A. Witkin. The previous document presents mathematically a method for executing numerical integration more rapidly and effectively in cloth animation. This method is characterized by proposing an implicit integration technique having stability superior to conventional explicit integration techniques and solving calculation of the implicit integration technique via conversion into a linear system. However, since the previous method is mainly aimed to accelerate calculation speed rather than to improve mass-spring modeling, the subject of this method is different from that of the invention.